Ch.11 - Liquids, Solids & Intermolecular Forces

Problem 94

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Chapter 11, Problem 94

A sealed flask contains 0.55 g of water at 28 °C. The vapor pressure of water at this temperature is 28.35 mmHg. What is the minimum volume of the flask in order that no liquid water be present in the flask?

Verified step by step guidance

Convert the mass of water from grams to moles using the molar mass of water (18.02 g/mol).

Use the ideal gas law equation, PV = nRT, to find the volume. Here, P is the vapor pressure (converted to atm), n is the number of moles calculated in the previous step, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin (28 °C + 273.15).

Convert the vapor pressure from mmHg to atm by dividing by 760 mmHg/atm.

Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Rearrange the ideal gas law equation to solve for V (volume): V = nRT/P, and substitute the known values to find the minimum volume of the flask.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It indicates the tendency of molecules to escape from the liquid phase into the vapor phase. In this question, the vapor pressure of water at 28 °C is 28.35 mmHg, which is crucial for determining the conditions under which all liquid water will evaporate.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the volume of gas produced from the evaporation of water in the flask. By knowing the number of moles of water vapor and the vapor pressure, we can determine the minimum volume required to ensure no liquid water remains.

Molar Mass and Moles

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. For water, the molar mass is approximately 18.02 g/mol. Understanding how to convert grams of water to moles is necessary for applying the Ideal Gas Law and calculating the volume of vapor needed to prevent the presence of liquid water in the flask.

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Molar Mass Concept

Related Practice

Draw a heating curve (such as the one in Figure 11.36) for 1 mole of methanol beginning at 170 K and ending at 350 K. Assume that the values given here are constant over the relevant temperature ranges. Melting point: 176 K, Boiling point: 338 K, ΔH_fus: 2.2 kJ/mol, ΔH_vap: 35.2 kJ/mol, C_s,solid: 105 J/mol·K, C_s,liquid: 81.3 J/mol·K, C_s,gas: 48 J/mol·K.

Open Question

Draw a heating curve (such as the one in Figure 11.36) for 1 mol of benzene beginning at 0 °C and ending at 100 °C. Assume that the values given here are constant over the relevant temperature ranges: Melting point 5.4 °C, Boiling point 80.1 °C, ΔHfus 9.9 kJ/mol, ΔHvap 30.7 kJ/mol, Cs,solid 118 J/mol⋅K, Cs,liquid 135 J/mol⋅K, Cs,gas 104 J/mol⋅K.

Textbook Question

Air conditioners not only cool air, but dry it as well. A room in a home measures 6.0 m × 10.0 m × 2.2 m. If the outdoor temperature is 30 °C and the partial pressure of water in the air is 85% of the vapor pressure of water at this temperature, what mass of water must be removed from the air each time the volume of air in the room is cycled through the air conditioner? (Assume that all of the water must be removed from the air.) The vapor pressure for water at 30 °C is 31.8 torr.

Based on the phase diagram of CO2 shown in Figure 11.39(b), describe the state changes that occur when the temperature of CO2 is increased from 190 K to 350 K at a constant pressure of (b) 5.1 atm, (c) 10 atm, and (d) 100 atm.

Textbook Question

Based on the phase diagram of CO₂ shown in Figure 11.39(b), describe the state changes that occur when the temperature of CO₂ is increased from 190 K to 350 K at a constant pressure of (a) 1 atm

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Open Question

Consider a planet where the atmospheric pressure at sea level is 2500 mmHg. Does water behave in a way that can sustain life on the planet?